Method for unambiguous range estimation

ABSTRACT

A method of unambiguous range estimation is provided for use with a range imaging system that derives phase images from image pixels of a digital image. The method involves generating (a) a first phase image having one or more ambiguous phase intervals and (b) at least one additional phase image that is generated by shifting the phase intervals of the first phase image. Then at least one region of intersection between phase intervals in the two phase images is identified. Finally, the phase of at least one of the ambiguous phase intervals in the first phase image is adjusted based on values of the phase of the image pixels that belong to the region of intersection. As a result, the phase adjustment unwraps the phase ambiguity in the phase intervals of the first phase image.

FIELD OF THE INVENTION

The invention relates generally to the field of processing range imagescaptured by a range imaging system, and in particular to the estimationand unwrapping of phase images captured by a scanner-less laser radarrange imaging system.

BACKGROUND OF THE INVENTION

A scanner-less laser radar range imaging system is described in U.S.Pat. No. 4,935,616. The system described therein illuminates a sceneobject with an amplitude modulated laser source, wherein the amplitudemodulation is in the range of 10MHz. The image capture portion of thesystem includes a micro-channel plate that is capable of modulating theoptical signal reflected from the scene object. The phase shift of theintensity modulation reflected from the scene object can be calculatedby capturing two images, one without modulating the optical signal, andanother with the optical signal modulated by the micro-channel plate inphase with the same amplitude modulated frequency as used to modulatethe laser source. Both images are registered spatially, and thedifference between them is caused by the interference of the twomodulating wave patterns, which produces a dc signal proportional to thephase shift. Once the phase shift has been established, range to theobject can be computed.

Since the phase shift can only be determined modulo 27π the resultingrange can only be found to within one wavelength of the modulation ofthe laser. To calculate the range at each point in the image, thecorrect integer number of phase cycles must be added to each phasemeasurement; that is, the phase must be “unwrapped”. It is thereforedesirable to resolve the ambiguous (or wrapped) phase measurements todetermine unambiguous (or unwrapped) phase.

The unambiguous phase, in turn, can be used to calculate unambiguousrange. The aforementioned '616 patent suggests modulating the laser andreceiver with different frequencies in order to produce two range imageswith different modulating frequencies. This would yield rangeunambiguous to within one wavelength of the wave whose frequency is thegreatest common factor of the frequencies of the laser and receiver,which is a lower frequency than either of the two modulatingfrequencies. Even though this may reduce ambiguity problems in manysituations, they still exist albeit on a smaller scale.

There are two main types of methods for solving the phase ambiguityproblem: branch-cut methods and weighted least-squares methods.

Branch-cut methods (such as those described in Goldstein, Zebker, andWerner, “Satellite radar interferometry: two-dimensional phaseunwrapping”, Radio Science, Vol. 23, pp. 713-720, 1998; and Prati,Giani, and Leurati, “SAR interferometry: A 2-D phase unwrappingtechnique based on phase and absolute values informations”, Proc. Int.Geoscience & Remote Sensing Symposium IGARSS 1990, Washington, D.C., pp.2043-2046, 1990) use lines to connect phase inconsistencies (orresidues). Branch-cut methods fail to perform adequately when the numberof residues is high. They often resort to local averaging, which isundesirable because it can dampen high frequency information.Least-squares methods (such as those described in Ghiglia and Romero,“Robust two-dimensional weighted and unweighted phase unwrapping thatuses fast transforms and iterative methods”, Journal of the OpticalSociety of America, Vol. 11, pp.107-117, 1994; and Pritt and Shipman,“Least-squares two dimensional phase unwrapping using FFT's”, IEEETransactions on Geoscience and Remote Sensing, Vol. 32, pp. 706-708,1994) determine a phase finction that minimizes the error in thegradient estimates. If there are areas in the ambiguous phase image witha high noise content, nearby areas with a low noise content can bedistorted by a least-squares phase unwrapping algorithm.

SUMMARY OF THE INVENTION

An object of the invention is to provide a method of unambiguous rangeestimation without the drawbacks in the known branch-cut and weightedleast squares methods.

It is a further object of this invention to unambiguate (or unwrap) themeasured phase shifts using a morphological technique.

It is a further object of this invention to provide a method ofunwrapping phase shifts obtained by a scanner-less laser radar rangeimaging system that produces an image bundle (at least three imagescorresponding to distinct phase offsets of the capture device and/orillumination source).

The present invention is directed to overcoming one or more of theproblems set forth above. Briefly summarized, according to one aspect ofthe present invention, a method of unambiguous range estimation isprovided for use with a range imaging system that derives phase imagesfrom image pixels of a digital image. The method involves generating (a)a first phase image having one or more ambiguous phase intervals and (b)at least one additional phase image that is generated by shifting thephase intervals of the first phase image. Then at least one region ofintersection between phase intervals in the two phase images isidentified. Next, the phase of at least one of the ambiguous phaseintervals in the first phase image is adjusted based on values of thephase of the image pixels that belong to the region of intersection. Asa result, the phase adjustment unwraps the phase ambiguity in the phaseintervals of the first phase image.

Instead of using a path-following technique or a technique based on aleast-squares solution, this invention will resolve phase ambiguities bythe use of a “region-moving” algorithm. By utilizing a model whereambiguous phase is determined by capturing images from at least threedifferent phase shifts of either the illumination source (e.g., a laser)or the capture device (e.g., an intensifier) to obtain a wrapped phaseimage, a parameter in the model is then perturbed that spatially shiftsregions of ambiguity in the wrapped phase image.

Using morphological image processing techniques, the spatial movementsof the regions of ambiguity are followed. Appropriate phase offsets aredetermined by this region-moving technique, generating an unambiguousphase image. The advantage of this region-moving technique in relationto other phase-unwrapping techniques is that it determines unambiguousphase without distortions (i.e. given only the output of theregion-moving technique, the input can be found exactly).

These and other aspects, objects, features and advantages of the presentinvention will be more clearly understood and appreciated from a reviewof the following detailed description of the preferred embodiments andappended claims, and by reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a known range imaging system which can beused in the practice of the invention to capture a bundle of images.

FIG. 2 is a diagram of a method of computing an ambiguous range imagefrom an image bundle captured by the range imaging system shown in FIG.1.

FIG. 3 is an illustration a shift in a region of ambiguity.

FIGS. 4A and 4B are illustrations of the effect of using a region-movingalgorithm to determine appropriate phase offsets to remove ambiguitiesin the ambiguous range images captured in FIG. 2.

FIG. 5 is an illustration of a region of intersection between the twophase images shown in FIGS. 4A and 4B.

FIG. 6 is an illustration of the steps involved in unwrapping anambiguous range image in accordance with the invention.

DETAILED DESCRIPTION OF THE INVENTION

Because range imaging devices employing illumination sources with laserilluminators, and capture devices employing image intensifiers andelectronic sensors, are well known, the present description will bedirected in particular to elements forming part of, or cooperating moredirectly with, apparatus in accordance with the present invention.Elements not specifically shown or described herein may be selected fromthose known in the art. Certain aspects of the embodiments to bedescribed may be provided in software. Given the system as described inthe following materials, all such software implementation needed forpractice of the invention is conventional and within the ordinary skillin such arts.

In the following description, a preferred embodiment of the presentinvention will be described at least in part as a software program.Those skilled in the art will readily recognize that the equivalent ofsuch software may also be constructed in hardware. Because phaseunwrapping algorithms and methods are well known, the presentdescription will be directed in particular to aspects of such algorithmsand methods forming part of, or cooperating more directly with, thepresent invention. Other aspects of such algorithms and systems, andhardware and/or software for producing and otherwise processing theimage signals involved therewith, not specifically shown or describedherein may be selected from such systems, algorithms, components andelements known in the art.

Still further, as used herein, the computer program may be stored in acomputer readable storage medium, which may comprise, for example;

magnetic storage media such as a magnetic disk (such as a floppy disk)or magnetic tape; optical storage media such as an optical disc, opticaltape, or machine readable bar code; solid state electronic storagedevices such as random access memory (RAM), or read only memory (OM); orany other physical device or medium employed to store a computerprogram.

Referring first to FIG. 1, an range imaging system 10 is shown as alaser radar that is used to illuminate a scene 12 and then to capture animage bundle comprising a minimum of three images of the scene 12. Anilluminator 14 emits a beam of electromagnetic radiation whose frequencyis controlled by a modulator 16. Typically the illuminator 14 is a laserdevice which includes an optical diffuser in order to effect awide-field illumination. The modulator 16 provides an amplitude varyingsinusoidal modulation. The modulated illumination source is modeled by:

L(t)=μ_(L)+η sin(2πλt)  (Eq. 1)

where μ_(L) is the mean illumination, η is the modulus of theillumination source, and λ is the modulation frequency applied to theilluminator 14. The modulation frequency is sufficiently high (e.g., 10mHz) to attain sufficiently accurate range estimates. The output beam 18is directed toward the scene 12 and a reflected beam 20 is directed backtoward a receiving section 22. As is well known, the reflected beam 20is a delayed version of the transmitted output beam 18, with the amountof phase delay being equivalent to the distance of the scene 12 from theimage capture system. The reflected beam 20 is sensed by a photocathode24, which converts its amplitude variations into a modulated electronstream that strikes an image intensifier 26. The output of the imageintensifier 26 is modeled by:

M(t)=μ_(M)+γ sin(2πλt)  (Eq. 2)

where μ_(M) is the mean intensification, γ is the modulus of theintensification and λ is the modulation frequency applied to theintensifier 26. The purpose of the image intensifier is not so much tointensify the image, but rather to act as a modulating shutter. Uponentering the image intensifier 26, the electron stream first strikes athin conductive sheet 28 connected to the modulator 16, where theelectron stream is modulated by a modulating signal from the modulator16. The modulated electron stream is then amplified through secondaryemission by a microchannel plate 30. The intensified electron streambombards a phosphor screen 32, which converts the energy into a visiblelight image. The intensified light image signal is captured by a capturemechanism 34, such as a charge-coupled device (CCD). The captured imagesignal is applied to a range processor 36 to determine the phase offsetat each point in the scene. The phase term ω of an object at a range ρmeters is given by: $\begin{matrix}{\omega = {\frac{2\rho \quad \lambda}{c}{mod}\quad 2\quad \pi}} & \left( {{Eq}.\quad 3} \right)\end{matrix}$

where c is the velocity of light in a vacuum. The reflected light atthis point is modeled by:

R(t)=μ_(L)+κ sin(2πλt+ω)  (Eq. 4)

where κ is the modulus of illumination reflected from the object. Thepixel response P at this point is an integration of the reflected lightand the effect of the intensification: $\begin{matrix}{P = {{\int_{0}^{2\pi}{{R(t)}{M(t)}\quad {t}}} = {{2\quad \mu_{L}\mu_{M}\pi} + {\kappa \quad \pi \quad \gamma \quad {\cos (\omega)}}}}} & \left( {{Eq}.\quad 5} \right)\end{matrix}$

In the range imaging system disclosed in the aforementioned '616 patent,a reference image is captured during which time the micro-channel plate30 is not modulated, but rather kept at a mean response. In that case,equation (5) fundamentally is unchanged, though M(t) is now simply aconstant μ_(M). The range is estimated for each pixel by recovering thephase term as a function of the value of the pixel in the referenceimage and the phase image. There are several reasons why this approachis not robust. Included in this is the fact that the analysis dependsupon continuous values. The range estimation is based upon the portionof the phase image relative to the reference image. For digital systemsthe relative quantization of the phase image to the reference imagedecreases as the response of the reference image decreases. The systemis also somewhat noise sensitive.

A robust approach which overcomes the limitations of the method proposedin the '616 patent is described in copending application Serial No.09/342,370, entitled “method and Apparatus for Scannerless Range ImageCapture Using Photographic Film” and filed in the names of LawrenceAllen Ray and Timothy P. Mathers, which is assigned to the assignee ofthis application and which is incorporated herein by reference. Insteadof collecting a phase image and a reference image, the improved approachcollects at least three phase images (referred to as an image bundle).In the previous approach, the micro-channel plate 30 and the laserilluminator 12 were phase locked. The improved approach shifts the phaseof the micro-channel plate 30 relative to the phase of the illuminator12, and each of the phase images has a distinct phase offset. For thispurpose, the range processor 36 is suitably connected to control thephase offset of the modulator 16, as well as the average illuminationlevel and such other capture functions as may be necessary. If the imageintensifier 26 (or laser illuminator 14) is phase shifted by θ_(i), thepixel response from equation (5) becomes:

P _(i)=2μ_(L)μ_(M)π+κπγ cos(ω+θ_(i))  (Eq. 6)

It is desired to extract the phase term ω from the expression.

However, this term is not directly accessible from a single image. Inequation (6) there are three unknown values: the mean term μ_(L)μ_(M),the moduli term κγ and the phase term ω. As a result, mathematicallyonly three samples (from three images) are required to retrieve anestimate of the phase term caused by the distance to an object in thescene. Therefore, a set of three images captured with unique phaseshifts is sufficient to determine ω. For simplicity, the phase shiftsare given by θ_(i)=2πi/3; i=0,1,2. In the following description, animage bundle shall be understood to constitute a collection of imageswhich are of the same scene, but with each image having a distinct phaseoffset obtained from the modulation applied to the micro-channel plate.It should also be understood that an analogous analysis may be performedby phase shifting the illuminator 14 instead of the micro-channel plate30.

FIG. 2 shows stages in the computation of an ambiguous phase image fromthe image bundle. If images are captured with n≧3 distinct phase offsetsof the intensifier (or laser or a combination of both) these images forman image bundle 40. Applying Equation (6) to each image in the imagebundle and expanding the cosine term (i.e.,P_(i)=2μ_(L)μ_(M)π+κπγ(cos(ω)cos(θ_(i))−sin(ω)sin(θ_(i)))) results inthe following system of linear equations in n unknowns at each point:$\begin{matrix}{\begin{pmatrix}P_{1} \\P_{2} \\\vdots \\P_{n}\end{pmatrix} = {\begin{pmatrix}1 & {\cos \quad \theta_{1}} & {{- \sin}\quad \theta_{1}} \\1 & {\cos \quad \theta_{2}} & {{- \sin}\quad \theta_{2}} \\\vdots & \vdots & \vdots \\1 & {\cos \quad \theta_{n}} & {{- \sin}\quad \theta_{n}}\end{pmatrix}\begin{pmatrix}\Lambda_{1} \\\Lambda_{2} \\\Lambda_{3}\end{pmatrix}}} & \left( {{Eq}.\quad 7} \right)\end{matrix}$

where Λ=2μ_(L)μ_(M)π, Λ₂=κπγ cos ω, and Λ₃=κπγ sin ω. If only threeimages are used, this linear system of equations is well-determined andits solution lends itself to a wide variety of numerical algorithms. Inorder to minimize rounding errors, the algorithm used is the LUdecomposition with pivoting (which is described in Golub and Van Loan,Matrix Computations, Johns Hopkins University Press, 3^(rd) ed., 1996).Many other methods of solution exist; e.g. decomposition-substitutionmethods, computing an inverse directly, Cramer's rule, etc.; however,all of these methods perform an equivalent task. If more than threeimages are used, the linear system is over-determined and its solutionlends itself to a wide variety of least squares techniques. For example,if an image bundle comprising more than three images is captured, thenthe estimates of range can be enhanced by a least squares analysis usinga singular value decomposition (see, e.g., W. H. Press, B. P. Flannery,S. A. Teukolsky and W. T. Vetterling, Numerical Recipes (the Art ofScientific Computing), Cambridge University Press, Cambridge, 1986). Inparticular, a singular value decomposition is chosen (see Golub and VanLoan) because of its robustness against rounding errors. Many othermethods of solution exist; e.g. QR decomposition, Givens transformation,Lanczos transformation, modified Gram-Schmidt, transformation to aquadratic programming problem, etc.; however, all of these methodsperform an equivalent task.

This system of equations is solved by one of the aforementioned methodsof solution 42 to yield the vector Λ=[Λ₁, Λ₂, Λ₃]^(τ). Since thiscalculation is carried out at every (x,y) location in the image bundle,Λ is really a vector image 44 containing a three element vector at everypoint. The phase term ω is computed in block 46 at each point using thefour-quadrant aretangent calculation:

ω=tan⁻¹(Λ₃, Λ₂)  (Eq. 8)

The resulting collection of phase values at each point forms theambiguous phase image 48.

Once phase has been determined, range r can be calculated by:$\begin{matrix}{r = {\omega \quad \frac{c}{4\pi \quad \lambda}}} & \left( {{Eq}.\quad 9} \right)\end{matrix}$

Equations (1)-(9) describe the method of estimating range using an imagebundle with at least three images (i.e., n=3) corresponding to distinctphase offsets of the intensifier and/or laser. However, since co iswrapped into a principal phase interval (−ππ], the estimated range isambiguous to within one wavelength.

The principal object of the invention is to resolve phase ambiguities;i.e., to determine what integral multiples of 2π should be added to ω ateach pixel location to yield an unwrapped phase image. The phaseunwrapping method described in this invention spatially moves regions ofambiguity in the phase image by changing the principal phase intervalfrom (−π, π] to (−π+α, π+α] where |a|<π/2. FIG. 3 shows the shift in theprincipal phase interval. The original phase interval, (−π, π], is shownby an interval indicator 50, and the shifted interval (−π+α, π+α] isshown by an interval indicator 52. This shifting can be accomplished byletting the phase ω_(α){circumflex over (ω)}=α and modifying the valueof Λ₂ and Λ₃ in Equation (7) to become Λ₂=κπλ cos({circumflex over(ω)}+α) and Λ₃=κπγ sin({circumflex over (ω)}+α). Expanding the sine andcosine terms and manipulating algebraically yields:

Λ₃−Λ₂ tan α=sin {circumflex over (ω)}(cos α+sin α tan α)  (Eq. 10)

Λ₂+Λ₂ tan α=cos {circumflex over (ω)}(cos α+sin α tan α)  (Eq. 11)

Solving the equations in (10) and (11) for {circumflex over (ω)} yields:

{circumflex over (ω)}=tan⁻¹(Λ₃−Λ₂ tan α,Λ₂+Λ₃ tan α)  (Eq. 12)

Since {circumflex over (ω)}ε(−π,π], the phase shift ω_(α)={circumflexover (ω)}+αε(−π+α,π+α]. The ambiguity regions in the image of phaseshifts (o. (which will be denoted Ω_(α), for the remainder of thisdisclosure) have been moved spatially from those in the image of phaseshifts ω.

The phase unwrapping method described to this point will be seen tooperate upon two perturbed phase images, the aforementioned first phaseimage Ω_(α) perturbed by the phase shift a and a second phase imageΩ_(β) perturbed by a phase shift β. The second phase image Ω_(β) hasregions of ambiguity that are spatially moved by changing the principalphase interval from (−π, π] to (−π+β, π+β], where α<β. FIG. 3 also showsthis shift in the principal phase interval; the shifted interval (−π+β,π+β] is shown by an interval indicator 54. However, in its most generalsense, the phase unwrapping method described in this invention can beunderstood to operate upon two phase images, one phase image withunperturbed ambiguous phase, i.e, the aforementioned first phase imageΩ_(α) or second phase image Ω_(β) with either α=0 or β=0. In both thegeneral case with one perturbed phase image and the specific case withtwo (or more) perturbed phase images, the invention is practicedsimilarly, that is, by finding (as will be explained) regions ofintersection between the two phase images. (Also note that when α=0,then ω_(α)={circumflex over (ω)} for the “first” phase image, whichaccordingly is the “original” phase image derived from Equation (8).)

FIG. 4A shows the boundaries between regions in the first phase imageΩ_(α) (56) whose principal phase interval is (−π+α, π+α], and FIG. 4Bshows the boundaries between regions in the second phase image Ω_(β)(58), whose principal phase interval is (−π+β, π+β]. Tracking themovement of the ambiguity regions from image Ω_(α) to image Ω_(β), whereα<β without loss of generality, yields the appropriate offsets to unwrapthe phase image. The first step S100 in this process, as shown in FIG.6, is therefore one of generating first and second phase images Ω_(α),Ω_(β) from an ambiguous original phase image by respectively shiftingthe ambiguous phase intervals by first and second phase shifts α, β,wherein the two phase shifts are bounded by −π/2<α<β<π/2. The next stepS102 is to identify the ambiguity regions in image Ω_(α) and Ω_(β).Region boundaries exist where the phase shifts wrap; therefore any of avariety of edge-detection techniques can be used to find where thedifferences in phase approach 2π. It may also be necessary to employ amorphological technique to bridge boundary pixels together. Once allregions have been identified, each image can be represented as the unionof mutually exclusive regions: $\begin{matrix}{\Omega_{\alpha} = {\overset{m}{\bigcup\limits_{i = 1}}\Omega_{\alpha}^{(i)}}} & \left( {{Eq}.\quad 13} \right) \\{\Omega_{\beta} = {\overset{n}{\bigcup\limits_{i = 1}}\Omega_{\beta}^{(i)}}} & \left( {{Eq}.\quad 14} \right)\end{matrix}$

where Ω_(κ) ^((i)) is the i^(th) region of Ω_(κ) (any ordering), and mand n are the number of regions in Ω_(α) and Ω_(β), respectively.

If α and β differ significantly, then for every i=1,2 , . . . m, Ω_(α)^((i)) will overlap at least one region of Ω_(β) which overlaps at leasttwo regions of Ωα. Likewise, for every j=1,2, . . . n, Ω_(β) ^((j)) willoverlap at least one region of Ω_(α) which overlaps at least two regionsof Ω_(β). Referring again to FIG. 6, and without loss of generality, afirst region Ω_(α(l)) is chosen in step S104 to contain unwrapped phasevalues. Other regions of Ω_(α) can be unwrapped by the followingprocess. First, in step S106 a first region Ω_(β) ^((κ)) of the secondphase image Ω_(β) that overlaps both the first region Ω_(α) ^((l)) andanother second region in Ω_(α), say Ω_(α) ^((p)) of the first phaseimage is identified. (FIG. 4 illustrates the regions Ω_(α) ^((l)), Ω_(β)^((k)), and Ω_(α) ^((p)); FIG. 5 shows the region Ω_(β) with a region ofintersection between Ω_(β) ^((k)) and Ω_(α) ^((p))). If the pixels inΩ_(β) belonging to a region of intersection 60 (see FIG. 5) betweenΩ_(β) ^((k)) and Ω_(α) ^((p)) take on values in (π+α, π+β], which valuesare within an interval 62 a of the plot in FIG. 3, then in step S108 thepixels in Ω_(α) belonging to Ω_(α)(p) should be offset by 2π. If thepixels in Op belonging to the region of intersection 60 between Ω_(β)^((k)) and Ω_(α) ^((p)) take on values in (−π+β, π+α], which values arewithin an interval 62 b of the plot in FIG. 3, then (also in step S108)the pixels in Ω_(α) belonging to Ω_(α) ^((p)) should be offset by −2π.If any other regions of Ω_(β) overlap both Ω_(α) ^((l)) and anotherregion in Ω^(α), say Ω_(α) ^((q)), then an offset for Ω_(α) ^((l)) isdetermined in the same way.

Once the process has been completed for Ω_(α) ^((l)), Ω_(α) ^((l)) isexcluded from the set of regions making up Ω_(α), and the entire processis repeated for the other regions of Ω_(α), starting with the borderingregions of Ω_(α) ^((l)). However, new offsets that are determined mustbe added to the offsets of the current iteration's starting region ofΩ^(α). Once all regions of Ω^(α) have been examined in turn, the offsetsaccumulated for each region are added to the phase shift values ofΩ_(α), producing an unambiguous (unwrapped) phase image.

In summary, a technique of estimating unambiguous phase shifts using alaser radar range imaging system has been developed. After capturing atleast three images corresponding to phase offsets of the modulated lasersource or receiver, the phase shift of the intensity modulationreflected from an object can be calculated. This phase shift can be usedto calculate range to the object; however, phase shifts are ambiguous(they can only be determined modulo 2π). An additional parameter isintroduced into the phase calculation step. The perturbation of thisparameter combined with a morphological image processing techniqueidentifies regions where an additive offset should be applied in orderto remove phase ambiguities.

The invention has been described with reference to a preferredembodiment. However, it will be appreciated that variations andmodifications can be effected by a person of ordinary skill in the artwithout departing from the scope of the invention.

Parts List

10 range imaging system

12 scene

14 illuminator

16 modulator

18 output beam

20 reflected beam

22 receiving section

24 photocathode

26 image intensifier

28 conductive sheet

30 microchannel plate

32 phosphor screen

34 capture mechanism

36 range processor

40 image bundle

42 method of solution

44 vector image

46 four-quadrant arctangent

48 ambiguous phase image

50 original phase interval

52 first shifted phase interval

54 second shifted phase interval

56 first phase image

58 second phase image

60 region of intersection

62 a interval indicator

62 b interval indicator

S100-S108 steps

What is claimed is:
 1. A method of unambiguous range estimation for usewith a range imaging system that generates phase images corresponding torange information derived from image pixels of a digital image, saidmethod comprising the steps of: (a) generating a first phase imagehaving one or more ambiguous phase intervals; (b) generating at leastone additional phase image by shifting the phase intervals of the firstphase image; (c) identifying at least one region of intersection betweenphase intervals in the two phase images; and (d) adjusting the phase ofat least one of the ambiguous phase intervals in the first phase imagebased on values of the phase of the image pixels that belong to theregion of intersection, whereby the phase adjustment unwraps the phaseambiguity in one or more of the ambiguous phase intervals of the firstphase image.
 2. The method as claimed in claim 1 wherein the rangeimaging system generates an ambiguous original phase image correspondingto the range information and the first phase image is generated from theambiguous original phase image by shifting the phase intervals in theambiguous phase image by a phase amount α, and said at least oneadditional phase image is generated by shifting the phase intervals ofthe first phase image by a phase amount β, where α<β.
 3. The method asclaimed in claim 1 wherein the step (d) of adjusting the phase comprisesoffsetting the phase by ±2π.
 4. A method of unambiguous range estimationfor use with a range imaging system that generates phase imagescorresponding to range information derived from image pixels of adigital image, said method comprising the steps of: (a) generating afirst phase image having one or more ambiguous phase intervals, whereinimage pixels of the first phase image include a phase term that isderived from an algorithm operating on one or more images captured bythe range imaging system; (b) generating at least one additional phaseimage by including a phase shift in the algorithm that perturbs thephase intervals of the first phase image; (c) identifying at least oneregion of intersection between at least one phase interval in the firstphase image and at least one perturbed phase interval in the additionalphase image; and (d) adjusting the phase of at least one of theambiguous phase intervals in the first phase image based on values ofthe phase of the image pixels that belong to the region of intersection,whereby the phase adjustment unwraps the phase ambiguity in one or moreof the ambiguous phase intervals of the first phase image.
 5. The methodas claimed in claim 4 wherein the phase term in step (a) that is derivedfrom an algorithm operating on one or more images captured by the rangeimaging system is derived from a solution to a system of equationscorresponding to a bundle of three or more images captured by the rangeimaging system, and the step (b) of generating at least one additionalphase image includes a phase shift in the solution to the system ofequations that perturbs the phase intervals of the first phase image. 6.The method as claimed in claim 4 wherein the range imaging systemgenerates an ambiguous original phase image corresponding to the rangeinformation and the first phase image is generated from the ambiguousoriginal phase image by shifting the phase intervals in the ambiguousphase image by a phase amount α, and said at least one additional phaseimage is generated by shifting the phase intervals of the first phaseimage by a phase amount β, where α<β.
 7. The method as claimed in claim4 wherein the step (d) of adjusting the phase comprises offsetting thephase by ±2π.
 8. A method for unambiguous range estimation for use witha range imaging system that generates an original ambiguous phase imagehaving ambiguous phase intervals corresponding to range informationderived from image pixels of a digital image, said method comprising thesteps of: (a) generating first and second phase images from the originalambiguous phase image by respectively shifting the ambiguous phaseintervals by first and a second phase shifts, wherein the first phaseshift in the first phase image is less than the second phase shift inthe second phase image; (b) identifying ambiguity regions in the firstand second phase images, wherein each phase image is represented as aunion of mutually exclusive ambiguity regions; (c) selecting a firstambiguity region in the first image that contains unwrapped phasevalues; (d) selecting an ambiguity region in the second phase image thatoverlaps both the first and a second ambiguity region in the first phaseimage; and (e) adjusting the phase of the second ambiguity region in thefirst phase image based on the values of the pixels that belong to aregion of intersection between the ambiguity region in the second phaseimage and the second ambiguity region in the first phase image, wherebythe phase values are unwrapped in the second ambiguity region in thefirst phase image.
 9. A method as claimed in claim 8 wherein step (e)comprises the step of offsetting the phase of the pixels in the secondambiguity region of the first phase image by ±2π.
 10. A method asclaimed in claim 9 wherein the first and second phase shifts are denotedα and β, respectively, and α<β, and wherein the step (e) comprisesoffsetting the phase of the pixels in the second ambiguity region of thefirst phase image by 2π if the pixels in the intersecting region take onvalues in a phase interval (π+α,π+β], and by −2π if the pixels in theintersecting region take on values in a phase interval (−π+β, π+α]. 11.A method as claimed in claim 8 wherein step (b) comprises the step ofidentifying the boundaries of ambiguity regions with an edge-detectiontechnique.
 12. A method as claimed in claim 8 wherein steps (c) through(e) are repeated for each of the other ambiguity regions of the firstphase image in order to unwrap the phase values in these regions.
 13. Acomputer program product for unambiguous range estimation in a rangeimaging system that generates phase images corresponding to rangeinformation derived from image pixels of a digital image, said computerprogram product comprising a computer readable storage medium having acomputer program stored thereon for performing the steps of: (a)generating a first phase image having one or more ambiguous phaseintervals; (b) generating at least one additional phase image byshifting the phase intervals of the first phase image; (c) identifyingat least one region of intersection between phase intervals in the twophase images; and (d) adjusting the phase of at least one of theambiguous phase intervals in the first phase image based on values ofthe phase of the image pixels that belong to the region of intersection,whereby the phase adjustment unwraps the phase ambiguity in one or moreof the ambiguous phase intervals of the first phase image.
 14. Thecomputer program product as claimed in claim 13 wherein the rangeimaging system generates an ambiguous original phase image correspondingto the range information and the first phase image is generated from theambiguous original phase image by shifting the phase intervals in theambiguous phase image by a phase amount α, and said at least oneadditional phase image is generated by shifting the phase intervals ofthe first phase image by a phase amount β, where α<β.
 15. The computerprogram product as claimed in claim 14 wherein the step (d) of adjustingthe phase comprises offsetting the phase by ±2π.
 16. A range imagingsystem capable of unambiguous range estimation, said system comprising:(a) a range imaging apparatus that generates phase images correspondingto range information derived from image pixels of a digital image; (b)means for generating a first phase image having one or more ambiguousphase intervals; (c) means for generating at least one additional phaseimage by shifting the phase intervals of the first phase image; (d)means for identifying at least one region of intersection between phaseintervals in the two phase images; and (e) means for adjusting the phaseof at least one of the ambiguous phase intervals in the first phaseimage based on values of the phase of the image pixels that belong tothe region of intersection, whereby the phase adjustment unwraps thephase ambiguity in one or more of the ambiguous phase intervals of thefirst phase image.
 17. The system as claimed in claim 16 wherein therange imaging apparatus generates an ambiguous original phase imagecorresponding to the range information and the first phase image isgenerated from the ambiguous original phase image by shifting the phaseintervals in the ambiguous phase image by a phase amount α, and said atleast one additional phase image is generated by shifting the phaseintervals of the first phase image by a phase amount β, where α<β. 18.The system as claimed in claim 16 wherein the means for adjusting thephase comprises means for offsetting the phase by ±2π.
 19. The system asclaimed in claim 16 wherein the range imaging apparatus comprises ascannerless laser radar range imaging system.